There are a number of applications in which a value represented by a multibit digital word must be converted to a binary waveform. In some applications, the binary waveforms are utilized as control commands for regulating torque on precision instruments. For example, the control of gyros on a satellite requires rapid resolution of binary waveforms; the waveforms serve as the actual torquing voltage or current and drive power stage H-switches or I-switches.
Presently, binary waveforms are generated using delta sigma modulation or pulse width modulation. Delta sigma modulation systems produce a series of pulses each having a duration of frame .tau.. The number of pulses, such as at +5 volts, compared to the number of frames without pulses, or zero volts, resolves an input value over time T.sub.ds. Frame .tau. has a minimum duration based on the accuracy of switches which produce the discrete pulses.
After time T.sub.ds the system is strobed to accept a new input value. The input value can be viewed as a fractional value of time T.sub.ds : for example, where nine is the input value and sixteen frames constitute time T.sub.ds, the output value is 9/16 as shown by nine positive pulses produced over sixteen frames.
The generation of each pulse .tau. by a typical delta sigma modulation system may be expressed as follows. For an input value P which is expressed in M bits, A is the accumulated residual, and S is the successive residual; if (A+P) is less than 2.sup.M, where 2 is the radix, then EQU S=A+P (1)
and EQU output=0. (2)
Where the sum of A and P is equal to or greater than 2.sup.M, then EQU S=(A+P)-2.sup.M ( 3)
and EQU output=1. (4)
In other words, 2.sup.M is the threshold at or above which a nonzero output is provided. After the output is determined by either equation (1) or (3), S is assigned to A. This operation is repeated for a total of 2.sup.M times. During that period, the total number of positive pulses equals the input value P. If P is not altered during time T.sub.ds, EQU T.sub.ds =R.sub.ds =(2.sup.M)(.tau.) (5)
where R.sub.ds is the time interval for complete resolution of P using the delta sigma modulation system. R.sub.ds has a lower limit based on which is determined by the accuracy of the switches which produce the pulse train. Net resolution does increase over time, however, due to carry-over of residual values.
Pulse width modulation systems produce a waveform having a positive pulse width which represents the input value. Successive rising edges define interval T.sub.pw ; the falling edge occurs as a multiple of time increment .DELTA.t. A lower boundary is set for increment .DELTA.t by the maximum available clock rate and minimum possible switching time.
The operation of a typical pulse width modulation system may be expressed in terms of the occurrence of the falling edge of the positive pulse width. The time of occurrence of falling edge FE may be expressed as EQU FE=P(.DELTA.t) (6)
where P is the input value.
Unlike the delta sigma modulator, P cannot be altered during an interval. The resolution time R.sub.pw is always equivalent to interval T.sub.pw such that EQU T.sub.pw =R.sub.pw =(2.sup.N)(.DELTA.t) (7)
where N is the number of bits, that is, place positions, of the input value and 2 is the radix. In other words, a waveform having a single pulse width is produced for each input value; the time interval of that waveform depends on the predetermined maximum number of total input bits which are raised as a power of the radix.
An advantage of pulse width modulation is that increment .DELTA.t has a substantially shorter duration than frame .tau. because a drop or rise in current can be generated more rapidly and more accurately than the generation of a discrete pulse which contains both rising and falling edges. Based on typical switching constraints, frame .tau. has a duration of 10 .mu.sec while increment .DELTA.t has a duration of 0.2 .mu.sec. Since .DELTA.t is less than .tau., for N=M, comparing equations (5) and (7) reveals that EQU T.sub.pw =R.sub.pw &lt;R.sub.ds =T.sub.ds ( 8)
The pulse width modulation system is capable of resolving an N bit input value more rapidly than the delta sigma modulation system.
The drawback to the pulse width modulation system is that when any two of the values T.sub.pw, N, or .DELTA.t are specified, the third must follow due to equation (7). The increment .DELTA.t has a lower bound determined by the speed of the switches; once a switching technology has been selected, the optimum value for increment .DELTA.t becomes fixed. Therefore, large values of N requires long intervals for resolution, and long intervals T.sub.pw reduce the frequency of the AC ripple in the waveform, which is deleterious in any application of binary waveforms. The length N of the input value received by the pulse width modulation system is limited by how low in frequency the AC ripple can be allowed to reside for the particular application.
The delta sigma modulation system does not suffer from this limitation on the length M of the input value. The frequency of the AC ripple in the delta sigma modulated waveform is determined primarily by the value of frame .tau.. Large values of M require very long intervals for resolution, but the interval T.sub.ds has virtually no effect on the harmonic content of the AC ripple.